The coordinates of a moving particle at a time $t$ are given by $x = 5 \sin 10t$ and $y = 5 \cos 10t$. The speed of the particle is:

When a force of constant magnitude and a fixed direction acts on a moving object,then its path is

$A$ truck starts from rest and accelerates uniformly at $2.0 \; m s^{-2}$. At $t = 10 \; s$,a stone is dropped by a person standing on the top of the truck ($6 \; m$ high from the ground). What are the $(a)$ velocity,and $(b)$ acceleration of the stone at $t = 11 \; s$? (Neglect air resistance.)

Fill in the blanks given below:
$(a)$ At an angle of .......... the horizontal range of a projectile is maximum.
$(b)$ The angle between the instantaneous velocity and instantaneous acceleration of a particle moving in a circular path with constant speed is ..........
$(c)$ If $\overrightarrow{A} = 4\widehat{i} + 3\widehat{j}$,then $|\overrightarrow{A}| = ..........$

$A$ projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

$A$ ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of $120 \ m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is.